Most nitrogen atoms have a mass of 14u (hence 28u for N2), but a small percentage of nitrogen atoms have an extra neutron and thus an atomic mass of 15u. (We
refer to atoms of the same element but with different masses as isotopes of that element.)
Recently, scientists studying isotope data from the Cassini spacecraft have noticed that
the ratio of 15u nitrogen to 14u nitrogen is much larger than it is here on earth. Assuming
that Titan and the earth originally had the same isotope ratios, explain why the ratios
might be different today.

itan it is much further from the sun, so the transformation of Carbon into 14 carbon is very small, so there is no process that changes the relationship between ¹⁵N/¹⁴N,

Explanation:

If the relationship between ¹⁵N and ¹⁴N is different on Earth and titan, they indicate that the relationship is higher in casino.

The first thing to clarify that this transformational is due to changes at the nuclear level.

Specifically carbon by incidence of cosmic rays from the sun forming ¹⁴C, this atom is unstable and decays after its life span of 5730 years in ¹⁴N, on Earth it is much closer to the Sun so the amount of cosmic rays is much greater therefore the amount of nitrogen atom 14 increases whereby the ratio between the two isotopes of nitrogen decreases.

In the case of Titan it is much further from the sun, so the transformation of Carbon into 14 carbon is very small, so there is no process that changes the relationship between ¹⁵N/¹⁴N, The reactionary from Saturn is fundamentally in infrared that does not have energy to change the nuclear structure of the coal.

For which the most likely explanation is the absence of means to transform carbon into carbon 14  by the remoteness of Titan from the Sun

snell's law

refractve index = sin incidence / sin refraction